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  • GATE Syllabus for ME-Mechanical Engineering

    ENGINEERING MATHEMATICS

    Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigen vectors.

    Calculus: Functions of single variable, Limit, continuity and differentiability, Mean value theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green?s theorems.

    Differential equations: First order equations (linear and nonlinear), Higher order linear differential equations with constant coefficients, Cauchy?s and Euler?s equations, Initial and boundary value problems, Laplace transforms, Solutions of one dimensional heat and wave equations and Laplace equation.

    Complex variables: Analytic functions, Cauchy?s integral theorem, Taylor and Laurent series. Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial distributions.

    Numerical Methods: Numerical solutions of linear and non-linear algebraic equations Integration by trapezoidal and Simpson?s rule, single and multi-step methods for differential equations.

    APPLIED MECHANICS AND DESIGN

    Engineering Mechanics: Free body diagrams and equilibrium; trusses and frames; virtual work; kinematics and dynamics of particles and of rigid bodies in plane motion, including impulse and momentum (linear and angular) and energy formulations; impact.

    Strength of Materials: Stress and strain, stress-strain relationship and elastic constants, Mohr?s circle for plane stress and plane strain, thin cylinders; shear force and bending moment diagrams; bending and shear stresses; deflection of beams; torsion of circular shafts; Euler?s theory of columns; strain energy methods; thermal stresses.

    Theory of Machines: Displacement, velocity and acceleration analysis of plane mechanisms; dynamic analysis of slider-crank mechanism; gear trains; flywheels.

    Vibrations: Free and forced vibration of single degree of freedom systems; effect of damping; vibration isolation; resonance, critical speeds of shafts.

    Design: Design for static and dynamic loading; failure theories; fatigue strength and the S-N diagram; principles of the design of machine elements such as bolted, riveted and welded joints, shafts, spur gears, rolling and sliding contact bearings, brakes and clutches.

    FLUID MECHANICS AND THERMAL SCIENCES

    Fluid Mechanics: Fluid properties; fluid statics, manometry, buoyancy; control-volume analysis of mass, momentum and energy; fluid acceleration; differential equations of continuity and momentum; Bernoulli?s equation; viscous flow of incompressible fluids; boundary layer; elementary turbulent flow; flow through pipes, head losses in pipes, bends etc.

    Heat-Transfer: Modes of heat transfer; one dimensional heat conduction, resistance concept, electrical analogy, unsteady heat conduction, fins; dimensionless parameters in free and forced convective heat transfer, various correlations for heat transfer in flow over flat plates and through pipes; thermal boundary layer; effect of turbulence; radiative heat transfer, black and grey surfaces, shape factors, network analysis; heat exchanger performance, LMTD and NTU methods.

    Thermodynamics: Zeroth, First and Second laws of thermodynamics; thermodynamic system and processes; Carnot cycle. irreversibility and availability; behaviour of ideal and real gases, properties of pure substances, calculation of work and heat in ideal processes; analysis of thermodynamic cycles related to energy conversion.

    Applications: Power Engineering: Steam Tables, Rankine, Brayton cycles with regeneration and reheat. I.C. Engines: air-standard Otto, Diesel cycles. Refrigeration and air-conditioning: Vapour refrigeration cycle, heat pumps, gas refrigeration, Reverse Brayton cycle; moist air: psychrometric chart, basic psychrometric processes. Turbomachinery: Pelton-wheel, Francis and Kaplan turbines ? impulse and reaction principles, velocity diagrams.

    MANUFACTURING AND INDUSTRIAL ENGINEERING

    Engineering Materials: Structure and properties of engineering materials, heat treatment, stressstrain diagrams for engineering materials.

    Metal Casting: Design of patterns, moulds and cores; solidification and cooling; riser and gating design, design considerations.

    Forming: Plastic deformation and yield criteria; fundamentals of hot and cold working processes; load estimation for bulk (forging, rolling, extrusion, drawing) and sheet (shearing, deep drawing, bending) metal forming processes; principles of powder metallurgy.

    Joining: Physics of welding, brazing and soldering; adhesive bonding; design considerations in welding.

    Machining and Machine Tool Operations: Mechanics of machining, single and multi-point cutting tools, tool geometry and materials, tool life and wear; economics of machining; principles of non-traditional machining processes; principles of work holding, principles of design of jigs and fixtures

    Metrology and Inspection: Limits, fits and tolerances; linear and angular measurements; comparators; gauge design; interferometry; form and finish measurement; alignment and testing methods; tolerance analysis in manufacturing and assembly.

    Computer Integrated Manufacturing: Basic concepts of CAD/CAM and their integration tools.

    Production Planning and Control: Forecasting models, aggregate production planning, scheduling, materials requirement planning.

    Inventory Control: Deterministic and probabilistic models; safety stock inventory control systems.

    Operations Research: Linear programming, simplex and duplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM.

  • Life in the USA: US Regions and US States

    Life in the USA

    In a country that covers over 9 million square kilometers, it is not surprising to learn that regions that are separated by large distances will be noticeably different. Not only are there great differences in climate and landscape, but also in the people who live in each of these regions. The fifty states that make up the United States can be divided into six distinctive regions which are described below.

    The Northeast (Maine, New Hampshire, Vermont, Massachusetts, Connecticut, and Rhode Island)

    The first immigrants (or settlers) to the United States came to the Northeast region in the 17th century. These were mostly English Protestants, looking for freedom to practice their religion and political reform. Because the winters are cold and harsh, and the land not very flat or fertile, this region is not well suited for farming. Eventually manufacturing and trade became the most important contributors to the regional economy. This region is well known for its culture (with excellent theaters and museums) as well as its educational system (with some of the most highly rated and respect universities in the country). This region is also known for its mix of ethnic groups, including Irish, Italian, and many eastern Europeans.

    The Middle Atlantic (New York, New Jersey, Pennsylvania, Delaware, Washington, DC, and Maryland)

    The first settlers in this region were more diverse than in the Northeast. Not only were English Protestants included, but also English Catholics, Dutch, and Swedes. Although the weather is not quite as cold, farming was still difficult, so manufacturing and shipping became the dominant industries. Some of the most highly populated American cities (including the largest, New York city) are located in the Mid Atlantic, as is the nation’s capital (Washington, DC). Today finance, communications, and pharmaceuticals are some of the most important industries in the region.

    The South (Virginia, West Virginia, Kentucky, Tennessee, North Carolina, South Carolina, Georgia, Florida, Alabama, Mississippi, Arkansas, Louisiana, and parts of Missouri, Texas and Oklahoma)

    The first southerners were English Protestants, like the northeasterners, but they were less independent and revolutionary in their nature. With temperate weather and sprawling lands, the south was very conducive to farming and soon agriculture became the primary industry. Southerners are probably the most distinctive of all American regional groups, with more relaxed attitudes and traditional ways than their neighbors to the north. They are known for their hospitality. The climate and the landscape have led this region to become popular with American tourists, and also with retirees. Today farming has become less prominent, and manufacturing and tourism have contributed greatly to the economy.

    The Midwest (Ohio, Michigan, Indiana, Wisconsin, Illinois, Minnesota, Iowa, parts of Missouri, North Dakota, South Dakota, Kansas, Nebraska and eastern Colorado)

    The Midwest is the largest of the regions, with the most variation in weather. However, the land is almost entirely flat, and also very fertile, making it ideal for farming. The region is known as the nation’s “breadbasket” because of its abundant production of oats, wheat, and corn. The first immigrants were Americans from the east coast, as well as Europeans from Sweden, Norway, and Germany. Midwesterners are known for being honest, straightforward people of traditional values. The area is not densely populated, with fewer big cities than its neighbors to the east. The largest city is Chicago, known for its port, and for being a connection (through railroad lines and airline hubs) between the eastern and western United States.

    The Southwest (western Texas, parts of Oklahoma, New Mexico, Arizona, and Nevada)

     

    This region has had the least influence by European immigrants. Much of its culture has been defined by native Americans (also known as American Indians) and by the Spanish (most of the Southwest previously belonged to Mexico). The land is generally flat and dry, and the weather is very hot. The region has many deserts. The nation’s greatest natural wonder, the Grand Canyon, is located in this region. Also located here is Las Vegas, one of the world’s premier gambling centers.

     

    The West (western Colorado, Wyoming, Montana, Utah, California, Nevada, Idaho, Oregon, Washington, Alaska, and Hawaii)

     

    The first settlers in the West were the Spanish who established Catholic missions along the coast. This region has probably the most variation in landscape and climate. Mountain chains run from north to south, creating temperate, wet areas to the west, and harsher, drier areas to the east. This region contains much undeveloped land which is enjoyed by the locals for recreation. The west has the most varied mixture of immigrants of all the other regions. In some areas, Mexican and Asian influences are dominant over European influences. Westerners are known as the least traditional of Americans, and the most tolerant of change and differences. California is the nation’s most populous state, and is famous for its movie and high-technology industries.

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